The Mohr Circle for the passive case of a retaining wall carrying a sloping backfill is shown in FÃg.1. Consider an element subjected to a stress in the Ïƒ_{v }in the vertical direction and Ïƒ_{x} in the direction parallel to the backfill. As these stresses in one plane are parallel to the direction of another plane, these stresses are conjugate stresses and the planes are the conjugate planes.

The equivalent vertical stress-acting acting parallel to the surface of backfill is given by

Ïƒ_{ve }= Ïƒ_{v}cosi = Î³zcosi

Referring to the figure the coefficient of passive earth pressure can be written as:

We can also write:

CD = OC sini

OD = OC cosi

R = OC sinÉ¸

By substitution these values in the expression for K_{p} we get:

P_{p} = K_{p}Î³z cosi

K_{p} = K_{p} cosi ———–(1)

Where,

And is known as the coefficient of passive earth pressure.

If, Î±_{1} and Î±_{2} are the inclination of failure planes with horizontal as shown in figure 2 then,

Ï´_{f2} = Î±_{1} – Ï´_{2}

Î±_{1} = Ï´_{f2} + Ï´_{2}

Î¨ = -i + 2Ï´_{2}

But,

Hence,

And Similarly,

Where, CD normal to OA

and

The pressure diagram is shown in figure 3 for both active as well as passive cases.